In a multidimensional interactive graphics application it is necessary to detect whether any objects or primitives intersect a volume of interest called the picking volume. This is known as the picking problem. The picking volume may be a clipping volume for display purposes or it may be a separate, usually smaller, volume for selecting a primitive within the clipping volume. Typically, a picking volume is a volume enclosed by a plurality of planes and is usually cubical. Picking problems have traditionally been solved by clipping all the primitives with the picking volume using one of the commonly used clipping techniques. These clipping techniques typically utilize the Cohen-Sutherland coding technique to provide a trivial accept and reject test. However, if the test is unsuccessful in accepting or rejecting the primitive as being within the pick volume, the clipping techniques then typically calculate the intersection of the primitive with the picking volume. which is a computationally intensive task.